An example to share population mean estimation

serving time example

##import required modules
import numpy as np
import scipy.stats as stats
import math

sample_size = 30 #known from the sample collected by the manager
population_size = 1184 #known in this specific case therefore required for fpc calc

sample_std = 4.46 #standard deviation of all sample means
point_estmate = 55.45 #as we take more and more samples the sample mean would converge to population mean
standard_error = sample_std/ np.sqrt(sample_size) #formula is slightly different relative to population proportion estimation

##Finite Population Correction (fpc)
fpc = round(np.sqrt((population_size - 30) / (population_size - 1)),2)
##fpc is seldom used when population size is unknown and we only have sample mean and sample standard deviations
standard_error_fpc = fpc * standard_error #standard error post accounting for fpc effect

upper_limit = round(point_estmate + (stats.norm.ppf(0.975) * standard_error_fpc),2) #upper side of the interval
lower_limit = round(point_estmate - (stats.norm.ppf(0.975) * standard_error_fpc),2) #lower side of the interval

print("We are 95% confident that the average time taken to serve customers in the restaurant who receive orders lies between {}. & {}.".format(lower_limit, upper_limit))